If you had to pick a jazz musician – or any other kind of social deviant – out of an identification parade, you almost certainly wouldn't go for the boyish and sprucely groomed Gwilym Simcock. A lot of jazz musicians acquire an air of embattled road-weariness, which they couple with a deadpan Bill Baileyish relish for the bleakly ludicrous – but not Simcock. He hits 30 next month, but still has a tendency to look at the world around him as if seeing it for the first time.

That natural ingenuousness is sharply contradicted by the force with which Simcock has hit the ground and run in the seven years since he left the Royal Academy of Music. He's been called "dazzling" by composer Mark-Anthony Turnage and "a creative genius" by Chick Corea. He was the first jazz musician ever to be invited on to the BBC's New Generation Artists scheme; has already premiered his own piano concerto at the Proms; written big-band swing pieces with a canny, old-school arranger's adroitness; runs his own world-class cross-genre trio, and a lot more. Now, alone on Europe's concert stages, Simcock is revealing the all-original solo music from Good Days at Schloss Elmau, his debut for the ACT label, once home to the late Esbjörn Svensson.

He is greeted with solicitous warmth in the Italian restaurant where we meet for lunch – he's a regular. Simcock is currently in transit from Heathrow to home after playing in Zurich. He says some of the fiendish polyphonal parts he's written for the project were daunting live assignments. The jazz improvisations, journeys into free-fall though they were, felt like welcome respites for him.

Simcock is the only child of an arts-devoted teacher mother and a father who played Sunday-chapel organ. He was born in a Welsh village but raised in Stoke-on-Trent, where his mother Ann left work to home-school him. A parental enquiry to the National Association for Gifted Children when he began to reveal his piano prowess and perfect pitch led to junior Saturday-morning classes at London's Trinity College of Music, where he also took up the french horn.

"It was a five-o'-clock-Saturday-morning start for my parents and me from Stoke, for what was just a 40-minute musicianship lesson at first," Simcock says. "All my childhood they made sacrifices like that. Then when I was nine I got into Chetham's, the Manchester music school. I was a day pupil, but the first five nights you had to board, as an introduction. The first night at midnight I called my Mum from the communal phone on the stairwell, really upset and wanting to go home. She said, 'OK, we'll come and pick you up, but if we do, they won't let you go to the school.' It was a pivotal moment, and I stuck with it. If I had gone home, things might have turned out very different."

Simcock came to love Chetham's, which is where he met the former Loose Tubes bassist and composer Steve Berry, who taught improvisation classes. It was Berry who introduced the teenage Simcock to jazz. "I was amazed," Simcock says. "I was already uneasy with the competitiveness of the classical world, and being shut away alone in a practice room for hours at a time. I could immediately hear that jazz was a communal music, and one with a different take on what was right or wrong."

Simcock won the only piano place on the 1999 jazz course at the Royal Academy. After he graduated, Stan Sulzmann, one of his teachers, eased Simcock in to Kenny Wheeler's big band for the trumpeter's 75th-birthday tour, on which trip he met legendary alto saxist Lee Konitz and briefly toured in an ensemble with him.

"We'd be in cabs at crack of dawn, him talking about working with Lennie Tristano and Miles Davis, me half asleep," Simcock says, "and then waking up and suddenly realising: 'My God, this is one of the huge legends of the music I love so much.'"

Simcock's playing is often compared to that of Keith Jarrett (a link all the more likely after his astonishing contrapuntal storms on the new solo album), which he takes simultaneously as a compliment, an irritant and an inevitability, considering they were both childhood piano prodigies immersed in the classical repertoire. He pays tribute to Jarrett on the gracefully light-stepping Northern Smiles (name-checking Jarrett's tune Southern Smiles), but he also unreservedly admires such European jazz and classical pianists as Iiro Rantala and Władysław Sendecki, with the latter's headlong confidence in exploring crossovers a major inspiration.

"I get nagging voices in my head sometimes," Simcock says, "that people are waiting for me to fail, that I'm too conventional, or that I should be more out there and avant-garde. As soon as the idea I'm doing something wrong gets into my head, it needs no second asking, and I can get very down, so it's something I need to grow up about. I do try to keep up with artists who are coming from places very different to mine, like the pianist Vijay Iyer, who's fantastic. But I know I can't be the kind of jazz musician who improvises on Radiohead, or explores rhythm at the expense of melody and harmony. It's interesting, but it isn't me – and if it isn't me, I won't be able to make it work for the audience, either."

Whatever kind of musician he is, or isn't, Simcock remains zealously committed, in his ingenuous way. "This is all life and death to me, it's my purpose" he says, as if commenting on the weather. "If I couldn't do it, I probably would have to jump off a cliff. It's what I think about when I wake up and what I think about before I go to bed. It goes into everything I write and perform. All I want is for people to sense that when I play. Whether they like it or not, I hope they'll hear how much it means to me."

Gwilym Simcock plays solo at the Forge, Delancey Street, London (020 7383 7808) on Tuesday. Good Days At Schloss Elmau is out now on ACT.

Bridging the divide: five classical/jazz pioneers

Art Tatum (1909-1956)

The blind jazz keyboard legend so comprehensively virtuosic that even classical piano stars like Leopold Godowsky and Sergei Rachmaninov were among his fans. Learning by ear at first, Tatum was taught formally at the Toledo School of Music – there was no jazz pianist to touch him for speed, precision and ideas from the 1930s to the 50s.

Bill Evans (1929-1980)

A key participant on Miles Davis's Kind of Blue, and a major influence in modal jazz and on modern pianists including Herbie Hancock, Keith Jarrett and Brad Mehldau. Also played flute and violin, studied formally at Southeastern Louisiana University, played Beethoven's Third Piano Concerto for his finals. Introduced harmonies from Debussy, Ravel, Scriabin and Satie into his jazz playing.

André Previn (1929-)

German-born, American-resident composer, conductor and pianist. His career has largely been in the classical-orchestral world, opera, and film composition, but in the 1950s he worked as a successful Tatum-influenced jazz pianist, with bestselling interpretations of My Fair Lady, and a series of Christmas carols with Julie Andrews.

Marilyn Crispell (1947-)

Philadelphia-born virtuoso and educator, trained in classical piano and composition at the New England Conservatory. Influenced by free-jazz piano pioneer Cecil Taylor, she became a key figure on the avant garde, working with Anthony Braxton, Barry Guy and others, but also plays works by contemporary-classical composers.

Keith Jarrett (1945-)

Child prodigy who made his first TV appearance at five. Studied with Eleanor Sokoloff at the Curtis Institute, worked with Art Blakey, Charles Lloyd and Miles Davis in jazz, made the bestselling solo piano record in all genres with 1975's improvised Koln Concert. Has has a parallel career as a classical composer and pianist since the 1970s. JF